AMC10 2027 - Self-practice Set 5 Question 7

Question 7

A sphere is tangent to both bases and the lateral surface of a right circular conical frustum as shown. The frustum's volume is twice the sphere's volume. What is the ratio of the lower base radius to the upper base radius?

Question illustration

$\frac32$
$\frac{1+\sqrt5}{2}$
$\sqrt3$
$2$
$\frac{3+\sqrt5}{2}$